We have a portfolio with 70% stock (beta 1.05) and 30% bonds (duration 5.5).
We adjust it to 60% stock (beta 1.00) and 40% bonds (duration 5.0) using futures.
So far so good.
At the end we compare the value of our adjusted portfolio with the value of the portfolio if we had adjusted through transactions using the securities themselves. The change in the stock portfolio is 3% and the change in the bond portfolio is 1%. So to conclude on the portfolio value we would have had if we transacted using the securities themselves, they apply 3% to 60% of stocks and 1% to 40% of bonds. They find a gap of $48,660 with the value of the portfolio adjusted with futures and they conclude that it’s not much.
Well I don’t find it fair. The computation of the portfolio adjusted through securities transactions disregards the fact that we adjusted the beta and the duration as well, not only the allocation. For me $48,660 is the result of mixing apples with oranges.
but aren’t you forgetting what the purpose of the mixing apples with oranges as you call it was?
if they wanted to do the same activity thro using securities - they would incur higher transaction costs (both on the buy & sell sides) - and higher commission payments as well. Those are avoided by using the futures contracts for hedging. That is the entire purpose of the chapter - with using the hedging. So get that instead of complaining they are comparing apples with oranges. If they did not get the same position they needed - were 48K short - but achieved that same without spending their client’s money on transaction costs / commissions - they have done a darn good job. And you as a prospective investment consultant need to learn that.
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on another post - you had said they cost of the future could change - yes that is possible. But by virtue of entering into the futures contract they are assured of the price at delivery. (Futures contract is an agreement …).
Yes of course I know that, and I don’t know which post you are referring to. You may have been misunderstanding what I said. The price of a futures contract to buy a stock at the end of December will be different at the end of April and at the end of July. So yes in that sense it changes. Of course once you have entered into the contract it does not change anymore. Please do not quote things out of context because it may totally change the meaning.
I am sorry if my English does not make it easy to understand me sometimes. It may lead to some approximations but I am doing my best. I use 3 to 4 different languages every day and I don’t manage to get everything right. Even my French tends to suffer from this situation…
We are not talking about the same thing. Let me explain better.
Portfolio A
Your original portfolio.
70% stock (beta 1.05) 30% bonds (duration 5.5)
Portfolio B
60% stock (beta 1.05) 40% bonds (duration 5.5).
Portfolio C-regular
60% stock (beta 1.00) 40% bonds (duration 5.0)
directly invested in the securities
Portfolio C-synthetic
Same as C-regular but using futures
Your goal is to go from portfolio A to portfolio C using synthetic positions i.e. futures.
You do so. Then you are asked to compare the market value of the portfolio you have create to a “portfolio had the transactions been done in the securities themselves”. So you are asked to compare the value of portfolio C-regular and C-synthetic, to prove that its not materially different.
Value of Portfolio C-synthetic:
You compute the value of portfolio A + the value of your futures positions (because that’s what portfolio C-synthetic is: portfolio A to which you added some futures). Ok no problem.
Value of Portfolio C-regular:
We apply the stock return of portfolio A and the bond return of portfolio A but with different weights (60%-40% instead of 70%-30%).
Well for me, this is portfolio B, not portfolio C-regular. There is not reason that the stock component of portfolio C-regular would have the same return as the stock component of portfolio A as it has a different beta. Same for bonds due to different duration. If we had just changed the weights and not the duration and beta, it would be ok.
the parts Portfolio C REgular, Portfolio C Synthetic are how you are dissecting the problem.
That is never the case. They have a target state (Your C-Synthetic) - and that is achieved thro using Futures.
So you would do Sell Stock futures to go from 70% Stock to 60% Stock (Final Target) + Sell Stock Futures to go from 1.05 Beta to 1.00 beta.
You would Buy Bond Futures to go from 30% bonds to 40% bonds (Final Target) + Sell bond futures to go from 5.5 Duration to 5 Duration.
If you see a post from S2000 Magician before you could achieve the target portfolio allocation + beta in 1 single step (and per CFAI you would get the marks you should be given).
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Now the final part you need to do - is did you achieve what you meant to achieve - if the stock rose X %, Futures rose some y % etc… and that is just evaluation of your position / target to see if you did what you wanted to do.
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The stock portion of your portfolio remained the same - since you did not change that position. You altered the allocation and achieved a final target beta of 1.05 (or whatever using Nf # of futures - and you are given a movement of the futures position (before and after) to evaluate your position).
You stock was exactly the same. You are confusing the situation by thinking that the beta of your stock position changed because your position / beta was modified using the futures contracts.Likewise for the bond position.